Use logarithms to solve exponential equations of the form ab^(ct)=d and evaluate with technology.
Solve exponential equations of the form \(a(b)^(ct)=d\) by isolating the exponential factor and taking logarithms
Problem
What is the solution to \(10^{2x}=500\) using common logarithms or technology?
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What this problem is really about
Use a logarithm that matches the exponential base to expose the exponent in one step. After the inverse operations cancel, solve the resulting linear equation by dividing the entire logarithm value by the exponent's coefficient. Do not move that division inside the logarithm, and verify with the exact expression.
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